You can update your system with unsupported packages from this untrusted PPA by …
Thanks for the tip. Seems like the most painless way to get a more recent version of Network Manager on 18.04 but the ‘unsupported/untrusted’ aspect makes me leery. For a short-term fix, I think I’ll upgrade from 18.04 to 20.04 on the existing old hard-drive; long-term fix will be Debian 10 on a new SSD. Should’ve paid closer attention to the Black Friday sales for computer components … 
UPDATE
Upgraded the production server from 18.04.5 to 20.04.1. Took a long time (over 90 minutes vs 20 minutes for a similar machine equipped with an SSD) but now Network Manager is at version 1.22.10 and there’s no longer any error/warnings about it. The ‘unhealthy’ indicator is gone but ‘unsupported’ remains for the obvious reason that this is still Ubuntu (not Debian).
Hopefully this will tide me over until I can get around to buying an SSD, installing Debian, and creating a completely new installation of Home Assistant Supervised.